This invention relates to a magnetic resonance(MR) imaging apparatus and, more particularly, to an MR imaging apparatus for imaging vessel structures using Phase Contrast(PC) angiography.
As is well known, a gradient with a net first moment imparts a phase shift to moving spins that is proportional to the velocity component along that gradient. The gradient is called a "flow encoding gradient".
The PC angiography generates vascular images by detecting changes in the phase of the blood's transverse magnetization using the flow encoding gradient.
Therefore, PC technique can distinguish flowing blood from surrounding stationary tissue.
To detect flow, PC angiography uses a bipolar gradient to encode a spin's velocity as a change of phase. The phase shift associated with such a gradient for the first acquisition is expressed as EQU .phi.=.gamma.GVT.tau. (1)
where .phi. is the phase shift induced by flow in the transverse spin magnetization, .gamma. is the gyromagnetic ratio of the spin, G is a gradient amplitude, V is the component of the spin's velocity in the applied gradient's direction, T is the center-to-center time interval between the two gradient lobes, and .tau. is the application time of each gradient lobe.
For subsequent acquisitions, this pulse sequence inverts the polarity of the bipolar gradient. The polarity of the gradient is now negative, making the equation EQU .phi.=-.gamma.GVT.tau. (2)
for the second acquisition.
A stationary spin will have identical(zero) phase shifts for each polarity of the flow-encoding pulse, resulting in a zero net phase shift. Thus, when the two vectors are subtracted, the result is zero.
The vector subtraction of signals from spins moving with constant velocity is quite different. The two signals have the same magnitude but differnt phase. Consequently, when the vectors are subtracted, the resulting vector is not zero. The result is a signal originating from vascular structures with nearly complete elimination of stationary tissues from the MR angiogram.
the value of .gamma.GT.tau. is called a first moment which designates a gradient potential causing a phase shift to a moving spin.
Therefore, if .gamma.GT.tau., -.gamma.GT.tau. for a x-axis are expressed as m.sub.x+, m.sub.x- respectively and a velocity of the moving spin along the x-axis is expressed as v.sub.x, then a phase shift .phi..sub.x+, .phi..sub.x- are expressed as EQU .phi..sub.x+ =m.sub.x+ v.sub.x ( 3) EQU .phi..sub.x- =m.sub.x- v.sub.x ( 4)
Thus the velocity is expressed as EQU v.sub.x =(.phi..sub.x+ -.phi..sub.x-)/(m.sub.x+ m.sub.x-) (5)
As shown in the above equation, the phase shift (.phi..sub.x+ -.phi..sub.x-) equals to the product of the velocity v.sub.x and the differential of the first moment .DELTA.m=(m.sub.x+ -m.sub.x-).
The differential value .DELTA.m, in order to acquire a high S/N ratio images, must be set to a reasonably large value so that the phase shift becomes typically .pi., but in order to prevent a phase dispersion which induces velocity noises, the absolute values of m.sub.x+, m.sub.x- must be set to a reasonably small value.
When 3-D images are acquired, two excitations are needed by each directions and thus six excitations, i.e. six-point method must be made.
Such method causes a long acquisition time.
In order to prevent the long acquisition time, so called four-point method is effective because only four excitations may be implemented. In the four-point method, four moments correspond to three points for the x, y and z direction respectively and the origin of the moment space(null phase).
In the four-point method, however, because the absolute values of the moments for the x,y and z direction, are too large, the phase dispersion may be induced and the S/N ratio of image data acquired using the four-point method may decrease.